Jochen Hecht and Chris Drury also scored for the Sabres, who won their second straight. The Sabres swept the four-game season series from the Rangers, and became the fifth team in NHL history to accumulate at least 20 victories through 25 games. Ottawa won 21 of its first 25 last season.
Three of the four games between the two teams went to overtime.
Michal Rozsival, Martin Straka and Michael Nylander scored for the Rangers, who lost their third straight, all in overtime.
After Briere deked New York goalie Kevin Weekes in the first round of the shootout, Miller blanked Nylander, Brendan Shanahan and Petr Prucha to win for the fourth time in his last six starts.
Down 2-1, Straka tied it for the Rangers at 7:20 of the third with a power-play goal. Forty six seconds later, Nylander gave New York its first lead with another power-play goal, lifting the puck over Miller at the top of the crease.
Drury tied it for Buffalo two minutes later, cutting across the ice to backhand the puck past Weekes.
Hecht, who just returned after missing three games with an inner ear infection, opened the scoring with his sixth of the year 17:09 into the first period. Picking up a loose puck near the left corner a couple of feet in front of the goal line, Hecht banked a shot off Weekes and into the net.
Campbell made it 2-0 just under two minutes into the second, lifting a backhand from the lower right circle over Weekes' left shoulder.
New York then began to pressure the Sabres, with Rozsival finally breaking through with his third of the season. Standing at the top of the right circle, Rozsival took Straka's pass and fired a slap shot that found the top-left corner of the net. The assist extended Straka's point streak to six games.
Buffalo mustered only three shots in the second, tying a season-low.
Weekes, who was making just his sixth start of the season and third against Buffalo, finished with 16 saves.
Buffalo defenceman Toni Lydman played in his first game since sustaining a neck strain on Nov. 10 against Florida.
The third period began under dimmer auxiliary lights after the building experienced a power surge that knocked out the main lights. Full power was restored about five minutes into the frame. The Buffalo area was experiencing high winds throughout the day and night.
Notes: Rangers forward Jason Ward missed his first game of the year with an ankle sprain. ... Sabres C Derek Roy is still out because of a broken hand. He is expected to return Tuesday when the Sabres play at Tampa Bay. ... Buffalo opens a season-long five-game road trip tomorrow in Washington. ... Rangers forward Ryan Callahan, who grew up 95 kilometres east of Buffalo in Rochester, made his NHL debut.